Adaptive Fuzzy Tracking Control for Uncertain Nonlinear Time-Delay Systems with Unknown Dead-Zone Input

Chiang-Cheng Chiang

doi:10.1155/2013/363748

Abstract

The tracking control problem of uncertain nonlinear time-delay systems with unknown dead-zone input is tackled by a robust adaptive fuzzy control scheme. Because the nonlinear gain function and the uncertainties of the controlled system including matched and unmatched uncertainties are supposed to be unknown, fuzzy logic systems are employed to approximate the nonlinear gain function and the upper bounded functions of these uncertainties. Moreover, the upper bound of the uncertainty caused by the fuzzy modeling error is also estimated. According to these learning fuzzy models and some feasible adaptive laws, a robust adaptive fuzzy tracking controller is developed in this paper without constructing the dead-zone inverse. Based on the Lyapunov stability theorem, the proposed controller not only guarantees that the robust stability of the whole closed-loop system in the presence of uncertainties and unknown dead-zone input can be achieved, but it also obtains that the output tracking error can converge to a neighborhood of zero exponentially. Some simulation results are provided to demonstrate the effectiveness and performance of the proposed approach.

Highlights

In general systems, there exist some nonsmooth nonlinearities in the actuators, such as dead-zone, saturation, and backlash [1,2,3,4,5,6,7]
In [13], the purpose of this direct robust adaptive fuzzy controller was to deal with a class of nonlinear systems containing both unconstructed state-dependent unknown nonlinear uncertain and gain
The main result of the proposed robust adaptive fuzzy tracking control scheme is summarized in the following theorem

Summary

Introduction

There exist some nonsmooth nonlinearities in the actuators, such as dead-zone, saturation, and backlash [1,2,3,4,5,6,7]. The motivation of this paper is to synthesize a controller to handle the tracking control problem for a class of uncertain nonlinear state timedelay systems in the presence of an unknown dead-zone input and unmatched uncertainties without constructing the deadzone inverse. In [13], the purpose of this direct robust adaptive fuzzy controller was to deal with a class of nonlinear systems containing both unconstructed state-dependent unknown nonlinear uncertain and gain. The problem of output tracking control is investigated for a class of uncertain nonlinear state time-delay systems containing unknown dead-zone input and unmatched uncertainties.

Problem Statement and Preliminaries

Adaptive Fuzzy Tracking Controller Design and Stability Analysis

An Example and Simulation Results

Conclusion